Mapping protein energy landscapes with amide hydrogen exchange and mass spectrometry: I. A generalized model for a two-state protein and comparison with experiment

Abstract

Protein amide hydrogen exchange (HDX) is a convoluted process, whose kinetics is determined by both dynamics of the protein and the intrinsic exchange rate of labile hydrogen atoms fully exposed to solvent. Both processes are influenced by a variety of intrinsic and extrinsic factors. A mathematical formalism initially developed to rationalize exchange kinetics of individual amide hydrogen atoms is now often used to interpret global exchange kinetics (e.g., as measured in HDX MS experiments). One particularly important advantage of HDX MS is direct visualization of various protein states by observing distinct protein ion populations with different levels of isotope labeling under conditions favoring correlated exchange (the so-called EX1 exchange mechanism). However, mildly denaturing conditions often lead to a situation where the overall HDX kinetics cannot be clearly classified as either EX1 or EX2. The goal of this work is to develop a framework for a generalized exchange model that takes into account multiple processes leading to amide hydrogen exchange, and does not require that the exchange proceed strictly via EX1 or EX2 kinetics. To achieve this goal, we use a probabilistic approach that assigns a transition probability and a residual protection to each equilibrium state of the protein. When applied to a small protein chymotrypsin inhibitor 2, the algorithm allows complex HDX patterns observed experimentally to be modeled with remarkably good fidelity. On the basis of the model we are now in a position to begin to extract quantitative dynamic information from convoluted exchange kinetics.

Figure 1.

HDX MS of CI2 under near-native conditions (pH 6.8): evolution of isotopic distributions of CI2 ions (+5 charge state) at 33°C (A) and exchange kinetics at different solution temperatures (B).

Figure 2.

HDX MS of CI2 under denaturing conditions (pH 11, 60% methanol): evolution of isotopic distributions of CI2 ions (+5 charge state) at 8°C (A) and 35°C (B); kinetics of the N→U transition deduced from the correlated component of the global exchange pattern at different temperatures (C); and kinetics of uncorrelated exchange component caused by local fluctuations within the native state at different temperatures (D). The inset on panel B illustrates resolution of the isobaric protein ions corresponding to an ²H-rich, ²³Na-free protein species (○) and an ²H-depleted ²³Na-adduct species (▾). The latter species has exactly the same isotopic makeup as an ionic species whose peak is marked with an open triangle in the full spectrum, apart from the ¹H/²³Na substitution.

Figure 3.

HDX MS of CI2 under mildly denaturing conditions (pH 10, 70% methanol): evolution of isotopic distributions of CI2 ions (+5 charge state) at 8°C (A); kinetics of the N→U transition deduced from the semi-correlated component of the global exchange pattern at different temperatures (B); kinetics of uncorrelated exchange component caused by local fluctuations within the native state at different temperatures (C); and gradual loss of apparent residual protection within the protein species with low ²H content at different temperatures (D).

Figure 4.

A schematic representation of potential energy diagrams for a simplistic model of a two-state protein under conditions favoring EX2 (A) and EX1 (B) exchange regimes. Protein dynamics is visualized as Brownian motion on the energy surface. Projections of trajectories of Brownian motion are shown at the bottom of each diagram (there were two escapes from the global minimum during the time of each simulation).

Figure 5.

Two alternative representations of microstates corresponding to local structural fluctuations within the native state, in which all structures are viewed as microstates comprising one activated state N* (A), and each such structure is viewed as a separate state, separated from others by significant energy barriers (B).

Figure 6.

Simulated HDX patterns for “simplistic” (A) and “realistic” (B) two-state systems carried out under the conditions mimicking EX2 exchange regime (P_U = 0.0005 and (P_ex^U = 0.05). Local structural fluctuations are totally ignored in A and accounted for in B using P_ex^N = 0.001. (48 out of 54 amides are assumed to be prone to local structural fluctuations.) Panel C shows time evolution of the model isotopic clusters during simulated HDX. Filled circles indicate the positions of the centroids of the simulated isotopic clusters in panel B plotted as a function of dimensionless time t* (see Materials and Methods). Error bars indicate uncertainty due to finite width of isotopic distribution caused by natural isotopic distribution of non-H elements expected for a typical protein of this size. A solid curve is obtained by substituting the numerical values used in the simulation to equation 7.

Figure 7.

Simulated HDX patterns for “simplistic” (A) and “realistic” (B) two-state systems carried out under the conditions mimicking EX1 exchange regime (P_U = 0.0005 and P_ex^U = 0.95). Local structural fluctuations are totally ignored in A and accounted for in B using P_ex^N = 0.001 (48 out of 54 amides are assumed to be prone to local structural fluctuations). Panel C shows time dependence of the relative abundance of the ²H-depleted species (○) and ²H-rich species (○). A solid gray curve is obtained by substituting the numerical values used in the simulation to equation 8. Panel D shows time dependence of the shift of the centroid of the simulated isotopic cluster in panel B (²H-rich species). A solid curve is obtained by substituting the numerical values used in the simulation to equation 9, assuming k* = k_intK_fluct.

Figure 8.

Simulated HDX pattern for a “realistic” (A) two-state system carried out under the conditions corresponding to EXX exchange regime (P_U = 0.0005 and P_ex^U= 0.60). Local structural fluctuations are accounted for by using P_ex^N = 0.001 (48 out of 54 amides are assumed to be prone to local structural fluctuations). Panel B shows time dependence of the shift of the centroid of the simulated isotopic cluster in panel A (²H-rich species). A solid curve is obtained by substituting the numerical values used in the simulation to equation 9, assuming k* = k_intK_fluct. Panel C shows time dependence of the relative abundance of the ²H-depleted species (○) and ²H-rich species (○); a solid gray curve is obtained by substituting the numerical values used in the simulation to equation 8. Panel D shows time dependence of the shift of the centroid of the simulated isotopic cluster in panel B (for species with low ²H content); a solid curve is obtained by substituting the numerical values used in the simulation to equation 10, assuming k* = k_intK_fluct.